Factor completely. $7 +14 x + 7 x^2=$
Explanation: First, we take a common factor of $7$. $7 +14 x + 7 x^2=7(1 +2 x +x^2)$ Now, let's factor $1 +2 x +x^2$. Both $1$ and $x^2$ are perfect squares, since $1=({1})^2$ and $x^2=({x})^2$. Additionally, $2 x$ is twice the product of the roots of $1$ and $x^2$, since $2 x=2({1})({x})$. $1 +2 x +x^2 = ({1})^2 + 2({1})({x})+({x})^2$ So we can use the square of a sum pattern to factor: ${a}^2 + 2( a)( b)+ {b}^2 =({a} + {b})^2$ In this case, ${a}={1}$ and ${b}={x}$ : $ ({1})^2 + 2({1})({x})+({x})^2 =({1} +{x})^2$ $\begin{aligned} 7 +14 x + 7 x^2 &=7(1 +2 x +x^2) \\\\ &=7(1 + x)^2 \end{aligned}$ In conclusion, the complete factorization is $7(1 + x)^2$ Remember that you can always check your factorization by expanding it.